Related papers: A Self-contained Analysis of the Lempel-Ziv Compre…
The Markov entropy decomposition (MED) is a recently-proposed, cluster-based simulation method for finite temperature quantum systems with arbitrary geometry. In this paper, we detail numerical algorithms for performing the required steps…
This thesis concerns sequential-access data compression, i.e., by algorithms that read the input one or more times from beginning to end. In one chapter we consider adaptive prefix coding, for which we must read the input character by…
We present a sufficient condition for a non-injective function of a Markov chain to be a second-order Markov chain with the same entropy rate as the original chain. This permits an information-preserving state space reduction by merging…
Technology progress in DNA sequencing boosts the genomic database growth at faster and faster rate. Compression, accompanied with random access capabilities, is the key to maintain those huge amounts of data. In this paper we present an…
In this work, a likelihood encoder is studied in the context of lossy source compression. The analysis of the likelihood encoder is based on a soft-covering lemma. It is demonstrated that the use of a likelihood encoder together with the…
Consider a hidden Markov chain obtained as the observation process of an ordinary Markov chain corrupted by noise. Zuk, et. al. [13], [14] showed how, in principle, one can explicitly compute the derivatives of the entropy rate of at…
We present the first sample compression algorithm for nearest neighbors with non-trivial performance guarantees. We complement these guarantees by demonstrating almost matching hardness lower bounds, which show that our bound is nearly…
We consider lossy compression of an information source when the decoder has lossless access to a correlated one. This setup, also known as the Wyner-Ziv problem, is a special case of distributed source coding. To this day, real-world…
We study the sensitivity of the Lempel-Ziv 77 compression algorithm to edits, showing how modifying a string $w$ can deteriorate or improve its compression. Our first result is a tight upper bound for $k$ edits: $\forall w' \in B(w,k)$, we…
We consider the problem of optimally compressing and caching data across a communication network. Given the data generated at edge nodes and a routing path, our goal is to determine the optimal data compression ratios and caching decisions…
The JPEG algorithm is a defacto standard for image compression. We investigate whether adaptive mesh refinement can be used to optimize the compression ratio and propose a new adaptive image compression algorithm. We prove that it produces…
We consider the problem of learned transform compression where we learn both, the transform as well as the probability distribution over the discrete codes. We utilize a soft relaxation of the quantization operation to allow for…
We present an informal survey (meant to accompany another paper) on graph compression methods. We focus on lossless methods, briefly list available pproaches, and compare them where possible or give some indicators on their compression…
We give an algorithm that learns a representation of data through compression. The algorithm 1) predicts bits sequentially from those previously seen and 2) has a structure and a number of computations similar to an autoencoder. The…
In a system that performs both encryption and lossy compression, the conventional way is to compress first and then encrypt the compressed data. This separation approach proves to be optimal. In certain applications where sensitive…
Large alphabet source coding is a basic and well-studied problem in data compression. It has many applications such as compression of natural language text, speech and images. The classic perception of most commonly used methods is that a…
In pattern matching on strings, a locate query asks for an enumeration of all the occurrences of a given pattern in a given text. The r-index [Gagie et al., 2018] is a recently presented compressed self index that stores the text and…
We introduce a novel concept of convergence for Markovian processes within Orlicz spaces, extending beyond the conventional approach associated with $L_p$ spaces. After showing that Markovian operators are contractive in Orlicz spaces, our…
Lossless data compression has been widely studied in computer science. One of the most widely used lossless data compressions is Lempel-Zip(LZ) 77 parsing, which achieves a high compression ratio. Bidirectional (a.k.a. macro) parsing is a…
A guessing wiretapper's performance on a Shannon cipher system is analyzed for a source with memory. Close relationships between guessing functions and length functions are first established. Subsequently, asymptotically optimal encryption…